To control mechanisms locally we consider the nilpotent approximations of the original control systems, [1]}. Although the appropriate configuration spaces have the same filtration, they are endowed with more symmetries in general, [2]}. We always have symmetries generated by Lie algebra of right–invariant vector fields and some additional symmetries that act non–trivially on the distribution. In nilpotent approximations of our control problems, there is a subgroup of symmetries which is isomorphic to the Lie group \(SO(3)\) , [3]}, [4]}. This leads us to the idea of local control in geometric algebra approach.
